I dislike both honestly. I was hyped for DK, but I just don't find them fun to play at all. Monks I generally dislike the theme and playing them. Granted I only really like half of the original classes anyways, so I guess there's a reason I don't have many alts. They're fine additions in general though.

I rerolled Monk this expansion from my Rogue that I played from Vanilla to Cata. Have to say, I'm glad I did, Monks are pretty well built. BrM is fun as all can be, and some crazy DPS for a tank, even with the flat out 10% nerf to BrM damage. WW is epic and can OT a boss for a few hits, enough to get your MT back up if needed. And MW...I haven't played, but I hear it's not that bad.

"It was Ivan, the Dwarf sentry who wore the novelty horse head mask because he thought it was funny. It wasn’t. Marvar was very sure on this point."

I'm not fond of the Pandaria expansion. Asian themes were never my thing. Last thing Asian themed I liked was Mortal Kombat. Not sure Pandaren were a necessary direction for the game. As for monks, we've had them in the game for awhile. Auchenai monks in TBC dungeons. Still, of the two, I prefer DK just for the sheer power and the plate gear. I understand some monks may fare better than some DKs, but thus far, it has been a DK to solo everything, including some current raid content.

Death Knights are cool at the moment and I think they perfectly fit in the game. What i'm saying might be influented by the fact that my main is a death knight though.
Monks are toxic to the game. It's not OP but it's insanely annoying to play against, they have too much tools to run away, their kit is too annoying, too much disarm/silences with a ridiculous CD.

Monks and DKs have the two best designed resource models of any tanking class, and were both built from the ground up to use Active Mitigation in cojunction with Primary, Secondary and Tertiary resources. (meaning it was not tacked on like Pallies/Warriors/Druids). for this reason DK and Monk game play feels very smooth and intuitive.

Some basic comparisons between DKs and Monks as tanks:

Runes ≈ Energy (excepts Runes are in essence three small energy pools, and Energy is one large pool, and Runes are more directly invoved in AM than Energy is)

Runic Power ≈ Chi (except that chi has less granularity, Chi is more directly involved in AM than RP, RP has larger pooling capacity, and RP is subject to RNG)

Rune Tap ≈ Expel Harm (pretty damn similar)

Blood Shield ≈ Shuffle (except BS always has a discrete valyue and can't be sustained 100% of the time, and Shuffle is non-discrete [i.e. is it percentage based] and can be up 100%)

Scent of Blood ≈ Elusive Brew (except that SoB is necessarily bound to Death Strike and is almost never held off, EB is usually timed for effectiveness)

DKs: Haste builds Runes (which are divided into three separate pools) -> Runes are spent to build Runic Power (which has one pool) -> Runic Power is dumped spent to regenerate Runes faster than haste can alone. DKs AM is based on spending Runes (Death Strike, and Death Tap), not on spending Runic Power (unless you use Conversion, but who uses Conversion?)

Monks: Haste builds Energy -> haste is dumped to build Chi -> Chi is spent on primary AM mechanics. Monk AM is based on spending Chi (BoK, Guard, Purifying Brew) more so than it is on dumping energy (Expel Harm).

Personal Analysis:

Monks have their AM distributed to all three resources: Primary (Expel Harm), Secondary (BoK, Guard, Purifying Brew), and Tertiaries (Elusive Brew, Gift of the Ox). DKs have an overwhelming majority of their AM tied into a single ability: Death Strike (including Blood Shield and Scent of Blood)

Monks must maintain 100% shuffle up time (easy enough, but requires mental focus), DKs can slack off and rely on armor, dodge and parry momentarily. A monk that is not paying attention is a dead Monk. An attentive Monk is nearly uncrushable.

Death grip is infinitely better than any other existing gap-closer. Clash is just wierd, although sometimes it's fun to Roll backwards just to Clash back into a crowd to stun the crowd with Leg Sweep is off cooldown)

Monks, like Paladins and Druids are more fun (for me) to dual spec with than DKs because I can be a healer OR a tank.

For DKs; Blood is better than it's ever been, but Frost and Unholy are awful abominations that are the end product of band-aid solution after band-aid solution from 3.0 to 4.0. Both seriously need some work put into them, particularly in the way of distinguishing them from eachother and making diseases not the most boring mechanic on the planet. DK talents, to me, also feel like worse and less significant choices than those of any other class.

I like the core of the class (that is, runes and runic power) but they're not interpreted very well by Frost or UH at the moment. Frost needs something to add to the Obliterate/Frost Strike/Howling Blast set, and Unholy needs to get away from being strike-based like every other DK spec happens to be. Pressing Dark Transformation every now and then aside, it feels very much the same as Frost because of the nearly identical functionality of Scourge Strike/Festering Strike compared to Obliterate and Death Coil compared to Frost Strike.